Grain boundaries (moderator's comment)

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Grain boundaries (moderator’s comment)

H.O.K. Kirchner

To cite this version:

H.O.K. Kirchner. Grain boundaries (moderator’s comment). Revue de Physique Appliquée, Société

française de physique / EDP, 1988, 23 (4), pp.475-478. �10.1051/rphysap:01988002304047500�. �jpa-

00245794�

Grain boundaries (moderator’s comment)

H.O.K. Kirchner

Institut für Festkörperphysik, Universität Wien, 1090 Boltzmanngasse 5, Vienna, ^Austria

Résumé. - Les joints ^de grains ^sont des obstacles effectifs pour le ^mouvement des dislocations. Les contraintes d’incompatibilité associée causent du glissement multiple.

Dans la vicinité du joint ^{le cristal se trouve dans un} état avancé du durcissement. Le cisaillement transgranulaire est quantitativement peu important.

Abstract. - Grain boundaries are an effective obstacle to dislocation motion. The

resulting incompatibility ^{stress causes} multiple slip. Adjacent ^{to the} grain boundary

the crystal ^{is in an advanced} stage ^of hardening. Transgranular slip ^is quantitatively unimportant.

1. Transmission of slip ^vs. hardening ^{of the} grain- boundary ^zone

An area of research where contact between phys-

icists and mechanics people ^{is not} only possible

but even necessary ^{is the} question ^{of the} impor-

tance of transgranular (as opposed ^to intragranu- lar) slip. By transgranular slip ^{we mean that} slip

occurs in one grain, proceeds up ^to the grain- boundary and continues into the other grain, pos-

sibly ^{even on another} slip system. Intragranular slip ^{means that} slip ^{does not} proceed ^{across the} grain-boundary. ^{From the work} presented by George

[1] ^and Rey [2] ^one concludes that even in bicrys-

tals which are favourably oriented for transmis- sion of slip ^{from one} grain ^{to the} other, ^such transgranular slip ^{is not} very important ^{as far as}

the overall transformation is concerned. The first to discuss this questions ^{seems to} have been Hirth [3]. ^He proposed ^a model in which ^a hardened zone exists next to the grain-boundary. ^The polycrystal

is considered as a twophase material in which, grosso modo, ^{the interior of the} grains ^{remain in}

a state of deformation comparable ^{to a} single crys- tal at the same strain, while the region adjacent

to the boundaries carries a flow stress that would be characteristic of a much more advanced stage ^of deformation in a single crystal. ^The hardening

there is due to the same processes that ^cause stage

II or III in a single crystal, but here in the

polycrystal dislocations do not block each other,

as in a single crystal, ^{but are blocked} by ^the grain-boundary ^and only subsequently block each other. As a consequence ^{of this even a small} amount of deformation cannot be provided by ^the operation ^{of one} slip-system, ^{but the} incompatibi- lity ^{at the} boundary necessitates the operation ^of

several slip systems ^{in each} grain, with all the

hardening ^entailed by ^it. Martinez-Hernandez, Kirchner, Korner, George ^{and Michel} [4] have, ^{as a}

matter of fact, given ^{evidence for} cross-slip, multiple cross-slip, secondary ^and tertiary slip

near the interface of a silicon bicrystal. ^Korner, Martinez-Hernandez, George and Kirchner [5] ^found also noncompact glide under the same circumstances.

With some experimental ^evidence already present, it would be interesting ^to apply Mughrabi’s [6] two

phase ^{model of} hardening ^{to this} situation. The film of El’Mrabat et al [7] shows the hardening

behaviour of the grain boundary ^{zone in situ in}

iron in a dynamic situation. Although ^one might suspect ^that in the bcc structure a wider variety

of slip systems should be available from the outset, and transgranular slip should be easier than, ^for example, ⁱⁿ silicon, it was never observed.

2. Crystallography ^of transmission of slip

Even if transmission of slip ^{from one} grain ^into

the other is quantitatively unimportant, ^{the details}

of the process ^are of great ^{interest from a} crystal- lographic point ^{of view. As} described by George [1]

the bulk dislocation (or rather its leading partial)

first has to enter the grain-boundary. After that it

can react with structural units or defects of the

boundary. Finally ^it might leave the boundary by ^a

similar reaction in which a lattice dislocation is formed in the other grain.

El Kajbaji [8] ^{and El} Kajbaji, Thibault-Desseaux, Martinez-Hernandez, Jacques ^and George [9] give ^an example ^{of such a} decomposition ^{of a bulk} Burgers

vector into two basic vectors of the DSC lattice.In their case the boundaryis perfect and free of extrin- sic dislocations.

If the boundary ^{is not} perfect and contains it-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01988002304047500

476

self some dislocations,passing ^{of a} bulk dislocation

across the boundary will involve some reaction with the extrinsic dislocation already present. Figs. ¹

and 2, kindly provided by ^{W. Skrotzki} [10] ^show such a reaction in germanium. ^After entering ^the boundary the matrix dislocation decomposes. ^The decomposition products ⁱⁿ turn react with disloca-

tions already present ^{in the} boundary, and finally

the new reaction product exits into the other grain.

3. Decomposed ^and dispersed dislocations Fractional vacancies

Pumphrey and Gleiter [13,14] ^were the first to observe that dislocations arriving from the bulk and

entering ^the grain-boundary ^can disperse ^either by glide [15] ^or climb [16,17]. ^The first process,

glide, is similar to a continous decomposition ^{of a}

discrete Burgers ^{vector as} envisaged in the Peierls model for the bulk.

The decomposition ^{into a} continous distribution of Burgers ^{vectors has never been seen so} far, ^but since the high resolution work was done on silicon and germanium ^where continuous spreading is neither

expected ^{nor observed even} for bulk dislocation,

Figure ^1. Passage of matrix dislocation with b

a

[O11]/2 through ^{aZ= 51} grain boundary ⁱⁿ germani-

um. Micrograph ^and schematic representation. ^The

screw dislocations (2) decompose ^{into two} secondary

dislocations each at A and C. After recombining ^at

B and D they exit into the second grain. ^{The re-}

combination is actually ^the result of an inter- action between ^one of the dissociation products and another dislocation of a set which was already present in the interface. See also refs. [ll]and

[12].

this is not surprising. Presumably ^{the continuous} spreading ^of grain boundary dislocations will be observed in metals ^where also the bulk cores are

dispersed. The second process, climb, is distinct-

ly different from what can occur in the bulk, and,

as a matter of fact, is impossible ^{in the bulk.}

From the experimental observation that the contrast of extrinsic dislocations disappears ^{within a}

certain time in the electron microscope, ^{one con-}

cludes that the dislocation must either have be-

come delocalized over a region ^{of the} order of the

extinction distance or must have decomposed ^dis- cretely ^into invisibly ^small Burgers ^vectors.

If the Burgers ^{vector of the} dislocation is

perpendicular ^{to the} interface, ^{this can occur} only by conservative or nonconservative climb.The fact that the discrete Burgers ^vector decomposes

into a discontinuous (or even continuous) distribu- tion of Burgers vectors which are fractions of the bulk one implies that there must have been absorp- tion of fractional point defects within the

boundary. Absorption ^{of one or more} complete bulk vacancies is necessary for the climb of ^one DSC lattice dislocation by ^one period ^{of the co-}

incidence lattice. Climb occurs, however, by steps smaller than that. The fractional vacancy mention- ed is just ^a vacancy ^{of the DSC} lattice, which is denser than the bulk one, but not fully occupied.

For example, in ^a 03A3 = 9 boundary ^{the DSC} vacancy is one ninth of the bulk vacancy [18].

4. Crystallography ^vs. elasticity

By ^now crystallographic studies of grain- boundary structures abound in the literature.

Molecular statics calculations [19] ^show that,

Figure 2. Overall view of Fig. ^{1. Entrance and}

exit of a bulk dislocation into or from a boundary might ^{be a} few thousand nanometers apart. Kindly provided by ^W. Skrotzki[10].

just ^{as a bulk} crystal ^{has a} particular ^structure,

each grain-boundary ^{has a} particular structure, with unit motifs, periodicities and all the other ingre-

dients of crystallography. ^The subject ^{of inter-}

facial crystallography ^{has been} considerably ^ad-

vanced by ^Bollmann [20,21] and others [22,23]. ^One might ask if the crystallography ^{of an} interface is really important ^for its mechanical behaviour. The answer probably ^{has to be a} qualified yes, insofar

as impurities and point ^{defects are} important ^for

the deformation process. Obviously, ^{when at low} temperatures transgranular slip is considered as

unimportant anyway, ^the particular ^{structure of the}

interface which is not transversed is of little

importance. If, however, ^at high temperatures ^im-

purities ^or point ^{defects are} involved in the de-

formation process, their interaction with and within

the grain boundary might ^{be all} important.

Deformation within the grains, ^{on the other} hand, might well beinfluenced by ^the fact that dis- locations find themselves in the proximity ^{of an} interface which modifies their elastic fields. Inter- action of the dislocations among each other is mod- ified às well. The state of the art of interfacial

elasticity ^{is far from} satisfactory, ^{suffice it to}

mention ^a few features which are qualitatively (and not only quantitatively) ^different from the bulk situation: Firstly, incompatibility ^{stresses caused} by ^{an interface cannot be defined as} neatly by pro-

jection ^{methods as internal or} external stresses (Simmons and Bullough [24]. Secondly, ^{unlike as in}

the bulk, ^where only dislocations,and ^{forces can} carry configurational ^forces (Cherepanov [25], Kirchner [26]), the interface presents ^{an elastic} inhomogeneity ^{and thus can} carry ^{a force as well}

(Eshelby [27]). ^A consequence ^of this is that an

interfacial dislocation is always associated with

a force enacted by ^one grain ^unto the other. The formal solution available for a dislocation along the interface between two semiinfinite crystals

(Barnett and Lothe [28], Kirchner and Lothe [29]) clearly shows this effect.

A mathematical consequence ^of this phenomenon is that the integral equation for ^an interfacial crack becomes ^a Fredholm equation of the second kind (rather than of the first kind, as for the bulk). ^Such equations ^are equivalent ^{to Hilbert} problems ^{and have} oscillatory ^solutions (Willis

[30], Rice and Sih [31]). This leaves some hither- to unresolved questions about the proper definition of a stress intensity ^{vector for} interfacial cracks.

5. Special ^vs. nonspecial ^boundaries

The group ^{at St.} Etienne ^was the first to

study extensively the behaviour of bicrystals ^and

the interface between them. Their technique ^allow-

ed the production ^of crystallographically ^{well de-}

fined interfaces. The Cornell group extended this

technique ^{to the} production ^{of thin} bicrystals

suitable for electron microscopy. ^{This led to ex-} tensive work on defects in or near these boundaries which are special because of their mode of pro- duction.

The question arises how relevant results ob- tained ^on special boundaries are for the boundar- ies present ^{in a} polycrystal. ^In spite ^{of the}

fact that it is far from clear that all or a size- able proportion ^of all boundaries in a polycrystal

are random, it would be extremely interesting ^to

know if, ^{as far as} the deformation behaviour of

polycrystals ^is concerned, the behaviour of

special ^and nonspecial boundaries is different.

The answer is probably ^{no if no} transgranular slip ^{occurs. On the other} hand, ^{as far as} chemical effects are concerned, ^the crystallographic ^struc-

ture (special ^{or not) is of} great importance.

References

[1] George, A., this ^volume.

[2] Rey, C., This volume.

[3] Hirth, J.P., Met. Trans. 3 ^{(1972) 3047.}

[4] Martinez-Hernandez, M., Kirchner, H.O.K., Korner, A., George, A., ^and Michel, J.P., Philosoph. Mag. ^A (1987) ⁱⁿ print.

[5] Korner, A., Martinez-Hernandez, M., George, A., and Kirchner, H.O.K., Philosoph. Mag.

Letters 55 ^{(1987) 105.}

[6] Mughrabi, H., ^Mat. Sci. Engineering 85 (1987) 15.

[7] El’Mrabat, B., Priester, L., Valle, R., Jouniaux, A., Marraud, A., this volume.

[8] ^El Kajbaji, M., Thesis (1986) Université de Grenoble.

[9] ^El Kajbaji, M., Thibault-Desseaux, J., Martinez-Hernandez, M., Jacques, ^{A., and} George, A., ^Rev. Phys. Appl. (1987) ^{to be} published.

[10] Skrotzki, W., private communication.

[11] Skrotzki, W., Wendt, H., Carter, C.B., ^and Kohlstedt, D.L., this volume.

[12] Skrotzki, W., Wendt, H., Carter, C.B., and Kohlstedt, D.L., Proc. Mat. Res. Soc. Symp.

41 ^{(1985) 261.}

[13] Pumphrey, ^{P.H., and} Gleiter, H., Philosoph.

Mag. 30 ^{(1974) 593.}

[14] Pumphrey, P.H., ^and Gleiter, H., Philosph.

Mag. 32 ^{(1975) 881.}

[15] Lojkowski, W., Kirchner, H.O.K., ^and Grabski, M., Scripta ^Met. 11 ^{(1977) 1127.}

[16] Valiev, R.Z., Gertsman, V. Yu., Kaibyshev, O.A., and Khannanov, Sh.Kh., phys. ^stat. sol.

(a) 77 ^{(1983) 97.}

[17] Valiev, R.Z., Gertsman, V.Yu., ^and Kaibyshev, O.A., phys. ^stat. sol., (a) 77 ^{(1983) 177.}

[18] Thibault-Desseaux, J., private communication.

[19] Vitek, V., Journal de Physique ^C6-43 (1982) 150.

[20] Bollmann, W., Crystal Defects and Crystalline Interfaces, Springer, ^Berlin (1970).

[21] Bollmann, W., Crystal lattices, Interfaces, Matrices, ^W. Bollmann, ^Genève (1982).

[22] Portier, R., Thalal, A., and Gratias, D., in:

Les joints ^de grains dans les matériaux, ^les éditions de physique (1985) ^69.

[23] Grimmer, H., ^and Warrington, ^{D.H., Acta} cryst.

A 43 ^{(1987) 232.}

[24] Simmons, ^{J.A. and} Bullough, R., ^in: Proc.

Conf.Fundamental Aspects of Dislocation

Theory, Gaithersburg, 1969, ^eds. J.A. Simmons,

R. de Wit and R. Bullough (Nat. Bur. Stand.

Spec. ^Publ. 317, ^vol. I, Washington) p. 89.

[25] Cherepanov, G.P., Engin. ^{Fract. Mech.} 14

(1981) ^39.

478

[26] Kirchner, H.O.K., in: Materials Science Mono-

graphs ^{20. The Structure and} Properties ^of Crystal Defects. Edited by ^V. Paidar and L.

Lejcek, Elsevier, Amsterdam (1984), p. 370.

[27] Eshelby, ^{J.D., Phil. Trans. A 244} (1951) ^877.

[28] Barnett, D.M., ^and Lothe, J., ^J. Phys. ^F:

Metal Phys. ⁴ (1974) 1618.

[29] Kirchner, H.O.K., ^and Lothe, J., Philosph.

Mag. ^A (1987) in print.

[30] Willis, J.R., ^{J. Mech.} Phys. ^Solids 19 (1971) 353.

[31] Rice, J.R., and Sih, G.C., J.Appl.Mech. 32

(1965) ^418.

Acknowledgement - This work was supported by ^the

Hochschuljubilâumsstiftung der Stadt Wien.